From A universal cellular automaton in the hyperbolic plane.
A switch is a point from which a track splits. So it starts with one track, and ends with two.
You can go in two directions on the switch:
- forward: 1 to one of 2 tracks
- backward: one of 2 to 1 tracks
The forward approach is called the "active" direction in the paper, the backward approach the "passive" direction.
There are 3 types of switches:
- fixed
- toggle
- memory
The fixed switch doesn't do anything, it always chooses the same output track on the active passage.
___ o
i ___/
\___
or
___
i ___/
\___ o
The toggle switch alternates between one track and the next depending on the last active passage output track.
___ o
1 i ___/
\___
___
2 i ___/
\___ o
___ o
3 i ___/
\___
___
4 i ___/
\___ o
...
The memory switch sends any active passage to the track which the last passive passage came in through. So it always goes in one direction if nothing comes in passively, and only changes to a new direction when the passive passage comes in from the alternative track.
___ i
1a o ___/
\___
___ o
2a i ___/
\___
___ o
3a i ___/
\___
___ o
4a i ___/
\___
...
___
1b o ___/
\___ i
___
2b i ___/
\___ o
___
3b i ___/
\___ o
___
4b i ___/
\___ o
...
Used for incrementing and decrementing.
The content of the elementary circuit is encoded by the position of the switches.
The (m) is the memory switch, the (t) the toggle switch.
________________ o1
/ \
i1___(m)/ \(t)___ i2
\ /
\________/_______ o2
Going in through the left on (m) is a read, going in from the right on (t) is a write.
There are many ways you can organize the switches, the layout. This is just one visualization.
Passing through the flip-flop switch performs a NOT operation on the content of the elementary circuit.